Die Kiwi im Kühlschrank ist noch nicht reif.

Yes. In this sentence, Kiwi is treated as a feminine noun, so the nominative singular article is die: die Kiwi.

German noun gender often has to be learned along with the word. For the fruit, die Kiwi is the usual form.

So:

• die Kiwi = nominative singular
• der Kiwi and das Kiwi would not be standard here for the fruit

Because all nouns are capitalized in German.

That is why you see:

• die Kiwi
• im Kühlschrank

This is one of the most noticeable spelling differences from English.

Im is a contraction of in dem.

So:

• im Kühlschrank = in dem Kühlschrank

This contraction is very common in German.

A few similar contractions are:

• am = an dem
• zum = zu dem
• beim = bei dem

Because this sentence describes location, not movement.

German uses:

• dative after in for a location: in dem / im Kühlschrank
• accusative after in for movement into something: in den Kühlschrank

Compare:

• Die Kiwi ist im Kühlschrank. = The kiwi is in the fridge.
• Ich lege die Kiwi in den Kühlschrank. = I put the kiwi into the fridge.

A useful rule is:

• where? → usually dative
• where to? → usually accusative

Because Kühlschrank is a masculine noun: der Kühlschrank.

After in with a location, German uses the dative, and the dative singular article for a masculine noun is dem.

So the steps are:

• basic noun: der Kühlschrank
• after in for location: in dem Kühlschrank
• contraction: im Kühlschrank

Because German main clauses normally follow the V2 rule: the finite verb comes in the second position.

Here the first position is the whole subject:

• Die Kiwi im Kühlschrank = position 1
• ist = position 2

Then the rest follows:

• noch nicht reif

So the sentence structure is:

• [Subject] + [finite verb] + [rest]

This is very typical German word order.

Because reif is a predicate adjective here: it comes after the verb sein and describes the subject.

In German, predicate adjectives do not take adjective endings.

So:

• Die Kiwi ist reif.
• Die Kiwi ist noch nicht reif.

But when an adjective comes before a noun, it does take an ending:

• eine reife Kiwi = a ripe kiwi

So compare:

• die reife Kiwi = the ripe kiwi
• die Kiwi ist reif = the kiwi is ripe

Noch nicht means not yet.

The word nicht means not, and noch adds the idea of still / as of now / yet.

So:

• nicht reif = not ripe
• noch nicht reif = not ripe yet

Without noch, the sentence would sound more like a simple statement of negation:

• Die Kiwi ist nicht reif. = The kiwi is not ripe.

With noch, it suggests the kiwi may become ripe later:

• Die Kiwi ist noch nicht reif. = The kiwi is not ripe yet.

Because nicht usually goes before the part it is negating.

Here it negates the adjective reif, so:

• nicht reif = not ripe

And with noch:

• noch nicht reif = not ripe yet

This placement is very natural in German when the adjective comes at the end of the clause.

Yes. The whole noun phrase Die Kiwi im Kühlschrank is the subject.

The core noun is Kiwi, and im Kühlschrank tells you which kiwi: the one in the fridge.

So it works like:

• the kiwi in the fridge

This means im Kühlschrank is attached to Kiwi, not mainly to the verb.

That is slightly different from:

• Die Kiwi ist im Kühlschrank noch nicht reif.

That version is also possible, but it puts the location more with the whole statement rather than tightly identifying the kiwi.

Yes. That is a complete sentence:

• Die Kiwi ist noch nicht reif.

Adding im Kühlschrank just gives extra information about which kiwi or where it is.

So:

• Die Kiwi ist noch nicht reif. = The kiwi is not ripe yet.
• Die Kiwi im Kühlschrank ist noch nicht reif. = The kiwi in the fridge is not ripe yet.

No. Reif often means ripe for fruit, but it can also mean mature in other contexts.

For example:

• Die Banane ist reif. = The banana is ripe.
• Er ist sehr reif für sein Alter. = He is very mature for his age.

In this sentence, because the subject is die Kiwi, the meaning is clearly the fruit-related one: ripe.